# 68.7 Functions for MeatAxe Matrices

The following functions that work for ordinary matrices in GAP also work for MeatAxe matrices.

`UnitalAlgebra( F, gens )` :

returns the unital F-algebra generated by the MeatAxe matrices in the list gens.

`Base( mtxmat )`:

returns a MeatAxe matrix whose rows form a vector space basis of the row space; the basis is in semi-echelon form.

`BaseNullspace( mtxmat )`:

returns a MeatAxe matrix in semi-echelon form whose rows are a basis of the nullspace of the MeatAxe matrix mtxmat.

`CharacteristicPolynomial( mtxmat )` :

returns the characteristic polynomial of the MeatAxe matrix mtxmat. The factorization of this polynomial is stored.

`Dimensions( mtxmat )` :

returns the list `[ nrows, ncols ]` where nrows is the number of rows, ncols is the number of columns of the MeatAxe matrix mtxmat.

`Display( mtxmat )` :

displays the MeatAxe matrix mtxmat (without reading into GAP).

`Group( m1, m2, ldots mn )`

`Group( gens, id )` :

returns the group generated by the MeatAxe matrices m1, m2, ldots mn, resp. the group generated by the MeatAxe matrices in the list gens, where id is the appropriate identity MeatAxe matrix.

`InvariantForm( mtxmats )` :

returns a MeatAxe matrix M such that X^{tr} M X = M for all MeatAxe matrices in the list mtxmats if such a matrix exists, and `false` otherwise. Note that the algebra generated by mtxmats must act irreducibly, otherwise an error is signalled.

`KroneckerProduct( m1, m2 )` :

returns a MeatAxe matrix that is the Kronecker product of the MeatAxe matrices m1, m2.

`Order( MeatAxeMatrices, mtxmat )` :

returns the multiplicative order of the MeatAxe matrix mtxmat, if this exists. This can be computed also by `OrderMeatAxeMat( mtxmat )`.

`Rank( mtxmat )`:

returns the rank of the MeatAxe matrix mtxmat.

`SumIntersectionSpaces( mtxmat1, mtxmat2 )` :

returns a list of two MeatAxe matrices, both in semi-echelon form, whose rows are a basis of the sum resp. the intersection of row spaces generated by the MeatAxe matrices m1 and m2, respectively.

`Trace( mtxmat )` :

returns the trace of the MeatAxe matrix mtxmat.

`Transposed( mtxmat )` :

returns the transposed matrix of the MeatAxe matrix mtxmat.

GAP 3.4.4
April 1997